Periodicity is omnipresent in physical as well as man-made processes. Signals arising in nearly every discipline—telecommunications, mechanics, biology, astronomy, atmospheric sciences, econometrics, nature, and more—are generally modulated, carrying corresponding signatures in both the temporal and spectral domain.
Cyclostationary processes constitute the most common class of nonstationary signals encountered in engineering and time series applications. Cyclostationary analysis, and its generalization, cumulant analysis, provide qualitatively better means for separating stochastic from deterministically-modulated radiation. Introduced nearly four decades ago, cyclostationary (CS) analysis provides means to intercept and classify a modulated waveform from a background signal such as noise or jamming. CS analysis lies at the core of electronic warfare (EW) and signal intelligence (SIGINT) intercept systems (W. A. Gardner, et al., “Cyclostationarity: Half a century of research,” Signal Proc., vol. 86, no. 4, pp. 639-697, April 2006). In contrast to simple spectral analysis, the CS approach provides superior spectral discrimination, allowing for considerable signal selectivity even in the presence of high levels of background noise and interference.
Signal detection, classification and interpretation (DCI) across the entire radiofrequency (RF) spectrum poses both fundamental and technological challenges. While high resolution, high-sensitivity DCI can be performed in a local (narrow-band) manner, such spectral analysis is generally not viable over the contiguous RF range (3 kHz-300 GHz) hosting modern communication and sensing applications. The wideband challenge is further compounded by the fact that emissions may contain bursty, frequency-hopping or spectrally-spread signals that complicate or prevent, even in principle, conventional averaging or fixed-band filtering techniques. As an example, a modern ultrawideband (UWB) emission is modulated at rates that exceed GHz, has a carrier that can be varied over 10s of GHz, and exists as a short duration burst. To exacerbate these problems, the signal can often be buried under intense RF traffic or may be deliberately jammed by band-matched waveforms. Similar to man-made emission, natural radiation can resemble UWB signaling in terms of bandwidth, spectral content and transience. In either case, the DCI challenge is similar: a faint signal must be detected across a wide spectral range, extracted from noise, classified, and ultimately reconstructed (demodulated) in order to extract useful content.
The wideband challenge can be addressed by devising a backplane of either a global (full-bandwidth), or multiple, spectrally-localized receivers. The former approach is clearly unrealistic for a band of interest that approaches 100 GHz or more. On the other hand, the latter strategy requires a band-tunable (scanning) or spectrally-segmented (banded) receiver architecture. A scanning approach not only does not look at the entire band in real time, but it also incorporates a tunable filter that inevitably imposes a performance limit: an increase in scanning rate is achieved at the cost of spectral resolution. In contrast, spectral segmentation (channelization) can circumvent this limitation, albeit at the expense of increased complexity: each sub-band must be served by a separate processing device and, in most cases, these need to be synchronized across the entire backplane. A conventional RF channelizer represents an example of a widely used spectrally-segmented DCI architecture. To be effective, a channelizer must combine low loss, high inter-band isolation and possess a rapid roll-off rate to avoid spectral information loss. Unlike an all-electronics channelizer, a photonic-assisted topology can address all these requirements while possessing THz-wide response—sufficiently wide to accommodate multiples of the contiguous RF spectral range. Notably, photonic-assisted channelizer architectures have been developed and used to demonstrate low-latency frequency monitoring and spectral analysis.
While near-ideal channelization is desirable, this is not sufficient for detection of UWB signals accompanied by natural or artificial interference. To detect a wideband signal in a noisy electromagnetic (EM) environment, it is necessary to discriminate a deterministic waveform from stochastic or quasi-stochastic radiation. A practical solution for noise discrimination was provided by modern CS and cumulant receivers. Intuitively elegant, CS analysis separates signal and stochastic interference using a simple criterion: a modulated waveform is periodically correlated, while noise remains inherently uncorrelated.
Unfortunately, the practical advantages of a CS analyzer fade when the signal bandwidth exceeds the speed of a viable electronic processor. Indeed, a modern CS receiver relies on a high-precision digitizer and real-time Fourier transformer in order to calculate the spectral correlation function (SCF). To analyze a wide RF range, a CS analyzer must possess an analog-to-digital converter (ADC) that matches the received signal bandwidth. In practice, this means that the detection of UWB signals emitted within a wide RF range (10s of GHz) also imposes a fundamental ADC resolution limit. At the same time, the real-time Fourier mapping of the received signal poses a more difficult technology challenge. While conventional (electronic) processors rely on a fast Fourier transform (FFT) algorithm, its complexity still prevents real-time processing at UWB rates. As a result, the combined (ADC/FFT) processing barrier imposes a strict limit on the cyclostationary receiver performance. A wideband ADC poses the first processing challenge that can be quantified in terms of precision, operating bandwidth and dissipation. Indeed, while real-time CS analyzers can be operated over sub-GHz bandwidths, none has approached a sizeable fraction of the contiguous RF range.
While an ADC capable of contiguous RF range (DC to 300 GHz) is unlikely to be constructed anytime soon, circuits operating beyond 20 GHz have been reported. Unfortunately, the advantages of CS analysis come at a cost of large computational complexity, posing fundamental detection challenges. In the case of modern ultrawideband signals, the requirements for persistent CS analysis are considerably beyond the processing complexity of conventional electronics.